Dynamic reactive power control of doubly fed induction generators (DFIGs) plays a crucially important role in maintaining transient stability of power systems with high penetration of DFIG based wind generation. Based on approximate dynamic programming (ADP), this paper proposes an optimal adaptive supplementary reactive power controller for DFIGs. By augmenting a corrective regulation signal to the reactive power command of rotor-side converter (RSC) of a DFIG, the supplementary controller is designed to reduce voltage sag at the point of common connection (PCC) during a fault, and to mitigate output active power oscillation of the wind farm after a fault. As a result, the transient stability of both DFIG and the power grid is enhanced. An action dependent cost function is introduced to provide real-time online ADP learning control. Furthermore, a policy iteration algorithm using high-efficiency least square method is employed to train the supplementary controller in an online model-free manner. By using such techniques, the supplementary reactive power controller is endowed with capability of online optimization and adaptation. Simulations carried out on a benchmark power system integrating a large DFIG wind farm show that the ADP based supplementary reactive power controller can significantly improve the transient system stability in changing operation conditions.